The shape and size of urban blocks

Two measures of shape compactness and fragmentation are coupled together into a plot that is defined as a two-dimensionalmatrix for classifying boundary shapes. Block shapes in a large sample of cities result in a swallowtail distribution in the matrix, which exposes two fundamental ways of transforming the basic compact block: by dissection, corresponding to large blocks with internal dendritic streets, and by stretching and bending, corresponding to serpentine blocks in hilly terrains and edge blocks along highways, railroads, and canals. The density of cases in each matrix zone reveals the realization of actual blocks out of the probable shape combinations as a manifestation of the social logic of urban form. The observed affinity between the shape and size of non-basic blocks in cities is used to formulate a model that explains them according to the constraints of arranging plots along the streets combined with the requirements for the intelligibility of navigation and the minimization of travel distance. Considering blocks as intra-street cells, the proposed block classification reveals important links between topological and geometric aspects of the street networks thus contributing to urban modeling, morphological classification, and comparative studies.